February 22, 2018
Organizational meeting
March 1, 2018
Guangqu Zheng,
Some basic Gaussian inequalities
Abstract : :In this talk, I will begin with Thomas Royen’s simple proof of the long-standing Gaussian correlation conjecture, which lies in the intersection of convex geometry and probability.
If time permits, I will mention another conjecture in the Gaussian world, the Gaussian (moment) product conjecture, and some recent progress.
March 8, 2018
Mariagiulia De Maria,
Congruent Numbers
Abstract : In this talk, I will talk about congruent numbers. After giving their definition and a brief historical introduction, I will explain various formulation of the problem. At the end, I will explain the correlation between the congruent numbers problem and the weak Birch and Swinnerton-Dyer Conjecture on elliptic curves.
March 22, 2018
Alexey Kalugin,
Geometric structures in conformal field theory.
Abstract : Chiral algebras were invented as geometric counterpart of vertex algebras. Notion of Chiral algebra plays crucial rule in the geometric Langlands correspondence. I am going to discuss basic definitions and constructions from this theory.
March 29, 2018
Daniel Berhanu,
Title: Tate's thesis
Abstract : After discussing the L-functions in the ad hoc fashion we will introduce the Local zeta integrals in which we will state the multiplicity one theorem in the form of distribution of a space of Schwartz-Bruhat functions on a given number field. Finally, the main result of Tate's thesis on the Global zeta integrals will get a treatment.
April 19, 2018
Luca Notaernicola,
Multilinear maps and secure key exchange in cryptography
Abstract : Recently, many cryptographers have put a lot of research in multilinear maps for cryptography. These are a generalization of bilinear maps, also known as bilinear pairings, and which have already been proved to have many applications in cryptography, as for instance a secure key exchange between three people, known as the 3-partite
one-round Diffie-Hellman key exchange by Antoine Joux, 2000, a direct generalization of the classical Diffie-Hellman key exchange protocol by Diffie and Hellman in 1976. Roughly speaking, by key exchange protocol, we mean that two (or more?) people want to share a common message (a key) by communicating over an insecure channel.
The goals of this talk are first to first define such multilinear maps; second to study some elliptic curve arithmetic and bilinear pairings (especially, the Weil pairing) on
elliptic curves, in order to, third, understand the key exchange protocol on elliptic curves by Joux. To conclude, a direct application of multilinear maps in order to
generalize these results.
April 26, 2018
Andrea Galasso,
Schur-Horn Problem and Symplectic Geometry
Abstract : The Schur-Horn problem is the following: if H is an Hermitian matrix with given eigenvalues, what could the vector of its diagonal entries be? In this talk I would like to explain how this problem is related to the convexity properties of the moment map in symplectic geometry.
May 3, 2018
Massimo Notaernicola,
Nodal surface of Laplacian eigenfunctions on the three-torus
Abstract : At the end of the 18th century, Ernst Chladni, a physicist and musician, made an interesting
discovery: he observed that when he excited a metal plate with the bow of his violin, he could
hear sounds of different frequency. The plate was fixed only at its center, and when Chladni put
some sand on it, then for each frequency a curious pattern appeared, today known as Chladni
figures. Some time later, Kirchhoff pointed out that these patterns correspond to nodal sets of
eigenfunctions of the biharmonic operator.
In this talk, we introduce random Laplacian eigenfunctions on the three-dimensional torus,
known as arithmetic random waves. More precisely, we prove a limit theorem for the nodal
surface of arithmetic random waves as the eigenvalue goes to infinity.
May 17 and 31 Mai, 2018
Jill Marie-Anne ECKER and Thi Hanh VO,
Divergent series - Summation and Regularization methods
Abstract :
Our talk concentrates on summation and regularization methods of divergent series. Particular focus will be put on the famous regularization of the divergent series 1+2+3+... to the value of -1/12, which is of uttermost importance in modern physics.
The talk splits into two sessions. The first session will be an introductory part, whereas the technical details will be given in the second session.
May 23, 2018
Guandalina Palmirotta,
A survey of proofs of the Malgrange-Ehrenpreis Theorem
Abstract : The Malgrange-Ehrenpreis Theorem states that every non-zero linear partial differential operator with constant coefficients in R^n has a fundamental solution. This theorem was a first evidence of the impact of distribution theory in its application to linear partial differential equations and, therefore, there were found several different proofs of it in subsequent years.
The aim of this talk is to shortly survey the different proofs and to focus on the classical proof of Ehrenpreis and Malgrange by giving some illustra
This semester the seminar is replaced by a week-end during which the Phd-students presented their research areas. The presentation where assessed by Christian Döbler and James Thompson.
The titles and abstracts of the talks can be downloaded here
The slides of some of the talks are avalaible below.
Jimmy Devillet, On quasitrivial symmetric nondreasing associative operations
Jill Ecker, Low-Dimensional Cohomology of the Witt and the Virasoro Algebra
Filippo Mazzoli, Classical applications of the H-Cobordism Theorem
Luca Notarnicola, The Arithmetic of Elliptic Curves
Massimo Notarnicola, Introduction to random variables and an example of random walk